SANDIA REPORT SAND2012-4750 Unlimited Release Printed January 2013 Computational Model of Miniature Pulsating Heat Pipes R. C. Givler and M. J. Martinez Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government. Approved for public release; further dissemination unlimited.
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SANDIA REPORT SAND2012-4750 Unlimited Release Printed January 2013
Computational Model of Miniature Pulsating Heat Pipes
R. C. Givler and M. J. Martinez
Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government. Approved for public release; further dissemination unlimited.
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Issued by Sandia National Laboratories, operated for the United States Department of Energy
by Sandia Corporation.
NOTICE: This report was prepared as an account of work sponsored by an agency of the
United States Government. Neither the United States Government, nor any agency thereof,
nor any of their employees, nor any of their contractors, subcontractors, or their employees,
make any warranty, express or implied, or assume any legal liability or responsibility for the
accuracy, completeness, or usefulness of any information, apparatus, product, or process
disclosed, or represent that its use would not infringe privately owned rights. Reference herein
to any specific commercial product, process, or service by trade name, trademark,
manufacturer, or otherwise, does not necessarily constitute or imply its endorsement,
recommendation, or favoring by the United States Government, any agency thereof, or any of
their contractors or subcontractors. The views and opinions expressed herein do not
necessarily state or reflect those of the United States Government, any agency thereof, or any
of their contractors.
Printed in the United States of America. This report has been reproduced directly from the best
2. Numerical Model ...................................................................................................................... 18 2.1 Model Geometry ............................................................................................................... 18
2.2 Liquid Phase...................................................................................................................... 18 2.3 Homogeneous Bubble Model ........................................................................................... 20
3.3 Effect of Evaporator Power ............................................................................................. 29 3.4 Initial Fill Ratio ................................................................................................................ 31
3.5 Orientation Effects ........................................................................................................... 34 3.6 Influence from a Tesla-type Valve .................................................................................. 36
3.7 PHP using Acetone .......................................................................................................... 37
Distribution ................................................................................................................................... 45
FIGURES
Figure 1. Schematic of a bottom-heated, 4-turn, single-loop PHP. .............................................. 13
Figure 2. A schematic identifying the participating interfacial physics and defining relevant
model parameters. ......................................................................................................................... 19
Figure 3. Vapor pressure variation with temperature for various working media. ....................... 21 Figure 4. 3D, 4-turn, PHP simulation results. ............................................................................... 25 Figure 5. 2D, 4- and 8-turn PHP simulation results. ..................................................................... 28
Figure 6. 2D, 4-turn PHP simulation results for reduced evaporator power, 0.64 W. .................. 30 Figure 7. 2D, 4-turn PHP simulation results for increased evaporator power, 7.5 W. ................. 32 Figure 8. 2D, 4-turn PHP efficiency vs. evaporator power. ......................................................... 33
Figure 9. Predicted thermal performance for a 2D, 4-turn, bottom-heated PHP with varying
liquid-fill fraction. ......................................................................................................................... 35 Figure 10. Simulation results for a 2D, 4-turn PHP with and without a Tesla-type valve. .......... 38
TABLES
Table 1. Material Properties (Baseline Case) ............................................................................... 26 Table 2. Initial and Boundary Conditions ..................................................................................... 26 Table 3. Effective thermal conductivites over simulation matrix ................................................ 39
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NOMENCLATURE
2D two space dimensions (x,y)
3D three space dimensions (x,y,z)
A area
c specific heat (J/kg-K)
C effective accommodation coefficient
CHP conventional heat pipe
e specific energy (J/kg)
E energy, (J)
F volume of fluid indicator
g gravity vector (m/s2)
h width (m)
h heat transfer coefficient (W/m2)
k thermal conductivity (W/mK)
l length (m)
L latent heat (J/kg)
m mass (kg)
M molecular weight (gm/mole)
MTO Microsystems Technology Office
NGES Northrop Grumman Electronic Systems
SNL Sandia National Laboratories
t time (s)
T temperature (K or C)
TGP Thermal ground-plane
p pressure (Pa)
PHP pulsating heat pipe
Q thermal power (W)
q thermal power density (W/m3)
R gas constant (J/mol-K)
u velocity vector (m/s)
u,v components of velocity (m/s)
u time-averaged value for u
V volume
w thickness (m)
x volume fraction
Greek symbols
density (kg/m3)
contact angle (radians)
viscous stress tensor (Pa)
Superscripts and Subscripts
bdy boundary
cond condenser
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eff ‘effective’
evap evaporator
init initial
l,liq liquid
s solid
sat thermodynamically saturated condition
surf surface
v, vap constant volume, vapor
0 initial value, baseline
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EXECUTIVE SUMMARY
Northrop Grumman Electronic Systems (NGES), the University of Missouri, and Sandia
National Laboratories (SNL) collaborated on a three-year, multi-faceted program to develop an
advanced thermal ground-plane (TGP). A well-designed thermal ground-plane is any device, of
planar configuration, that transports heat from a source to an ambient environment with high
efficiency. Activities at all three institutions were funded by DARPA/MTO.
SNL was tasked with model development to help direct the design of highly-efficient TGPs. This
report summarizes SNL’s portion of the total project. Our objective was to gain a working
knowledge of pulsating heat pipes (PHPs) through the development of a comprehensive model;
application of this model gave insight as to how PHPs operate and how various parameters
(geometrical configuration, fill ratio, materials, working fluid, orientation, etc.) affect thermal
performance. Also, in contrast to existing models that mostly consider tubular designs, we
consider PHPs milled or etched into a solid substrate as a prototypical design for cooling of
electronics.
The physical processes at play for a working PHP are highly coupled. Understanding PHP
operation is further complicated by the dynamic interplay between evaporation/condensation,
bubble growth and collapse or coalescence, and the coupled response of the two-phase fluid
dynamics among adjacent channel segments. This report documents results of an improved
numerical model for a PHP featuring a two-phase (liquid and its vapor) working fluid confined
in a closed-loop, serpentine channel etched in a solid copper plate. Our modeling approach
utilizes the FLOW-3D software (Flow Science, 2007). This new model includes relevant
physical processes common to the operation of any flat plate PHPs: two-phase heat, mass and
momentum conservation including dynamic bubble nucleation, evaporation and condensation
with latent heat effects, together with conjugate heat transfer with the etched substrate. Thus, for
the first time, the behavior of a working PHP can be accurately modeled. The model describes
qualitatively and predicts quantitatively performance characteristics and metrics; this was
demonstrated by favorable comparisons with experimental results on similar configurations,
discussed in Section 3 below. Application of the model also corroborated previously observed
behavior with respect to key parameters such as heat load, fill ratio and orientation. This work
advances the state-of-the-art for modeling PHPs.
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1. INTRODUCTION
A heat pipe is a passive device that enhances the transfer of heat from a region of higher
temperature (i.e. evaporator) to a region of lower temperature (i.e. condenser). Typically, a heat
pipe employs a working fluid confined within a sealed channel/compartment, in which the
working fluid cycles between its liquid and vapor states during heat pipe operation. The latent
heat associated with this change-of-phase greatly improves the efficiency of the device. Heat
pipes were developed in the 1960’s, motivated by the space program, as a passive device (no
external energy supply is required) capable of high heat transfer rates. Ever-increasing power
densities in semi-conductor electronics continue to motivate improvements to heat pipe design.
A typical configuration for a conventional heat pipe (CHP) is a sealed tube in which the cross
sectional flow area is partially occupied by a wick structure, usually attached to the tube walls,
while the remainder of the flow area is open. At the evaporator, the heat injected promotes
liquid evaporation, thereby reducing the moisture content in the wick and raising the local vapor
pressure, which drives vapor towards the condenser via the open flow area. At the cooler
condenser, vapor condensation raises the moisture content in the wick and releases its latent heat.
The wick plays a crucial role in the operation of CHPs; it moves liquid, via a capillary pressure
gradient, from the relatively wet condenser to the relatively dry evaporator. Critical to this cycle
of continuous operation is the ability of the wick to supply sufficient liquid to the evaporator. In
cases where a CHP is subject to high heat flux loadings the wick may be unable to supply
sufficient flow of liquid to the evaporator prompting a ‘dry-out’ condition, meaning all liquid has
been evaporated, leaving only a superheated vapor. In these instances, the heat pipe cycle loses
the latent heat effect for energy transfer, causing the evaporator temperature to rise sharply and
the performance of the heat pipe to decline. The consequence of this sequence of events can be
dramatic; the heat-producing device, which the CHP was dedicated to protect, will overheat and
may subsequently fail. This so-called “wicking limit” provides a functional, limiting, relationship
between the maximum heat flux (power) and CHP length, for a given wick, which the heat pipe
can achieve without dry-out. Thus, much of the research dedicated to the advancement of CHPs
has been in the area of wick design. Exotic wick designs can add construction expense. CHPs are
thus limited by wick design, the rate of heat transfer and the distance over which they can
perform.
Pulsating heat pipes (PHP’s, also called oscillating heat pipes or OHP’s) have been proposed as
an alternative to CHP’s; an important distinction is that a wick is not required. A common
design for a PHP is a capillary-sized tube or channel forming a closed, continuous flow loop and
containing a liquid and its vapor. The flow loop is configured in a serpentine fashion, with many
back-and-forth legs, resulting in a typically rectangular planform, which is heated at one end
(evaporator), while cooled at the opposite end (condenser), e.g. Figure 1. If the capillary
diameter is not too large, the fluid distributes itself into an arrangement of liquid slugs separated
by vapor bubbles (often referred to as plugs). During operation, heat input to the evaporator
expands existing bubbles and/or nucleates new bubbles, driving liquid and bubbles toward the
cooler condenser region, where vapor bubbles contract or collapse via condensation. The
evaporation/condensation cycle provides the motive force for the convective motion, though heat
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Figure 1. Schematic of a bottom-heated, 4-turn, single-loop PHP.
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is mainly transferred sensibly by the movement of hot liquid from evaporator to condenser.
These devices are called “pulsating” heat pipes because the evaporation/condensation process
happens as a non-equilibrium episodic/chaotic process, whose continuous operation requires
non-equilibrium conditions to exist in some, but not necessarily all, of the parallel channels at
any given instant of time. As with CHPs, no external power source is needed to either initiate or
sustain the fluid motion or the transfer of heat.
Compared to CHPs, the absence of a wick in a PHP results in several attractive features: (i.)
PHPs are simpler and cheaper to construct because exotic wick structures are not required, (ii.)
pressure losses associated with liquid flow through the wick structure are eliminated, and (iii.)
higher heat fluxes are possible with the elimination of limitations associated with wick-limiting
dry-out.
PHPs were invented by Akachi (1990), as disclosed in a U.S. patent, and investigations by him
and his co-workers continued during the 1990’s (Akachi et al., 1996, Miyazaki and Akachi,
1996, 1998). His invention described a device made from small-bore tubing as described earlier.
Akachi found that a check valve, used to promote uni-directional flow, improved performance.
Concerted experimentation and analysis by other groups began c. 2000. Zuo et al. (1999 &
2001) prototyped a hybrid PHP which featured a sintered wick to enhance performance, and a
copper prototype capable of dissipating up to 200 W/cm2; they reported an optimal liquid fill
ratio, xliq, of about 0.70 for their device. Khandekar et al. (2002) considered a flat plate heat pipe
with channels (rectangular cross section) that were milled into a thin aluminum plate; for
comparison, they also constructed a PHP of parallel tubes connected by copper U-turns. They
concluded that PHP operation is influenced by tilt-angle (with reference to the gravity vector),
liquid fill ratio and cross-sectional dimensions. The rectangular channels promote a strong
capillary force not found with circular tubes, because the liquid experiences enhanced wicking
along the channel corners. They also suggest that heat transfer across adjacent flow channels can
be detrimental to the maximum performance of the device. Khandekar and Groll (2004)
considered a one-loop PHP experiment as a primary building block for a multi-turn PHP. They
found: (i.) a number of distinct flow regimes that depend on the input power, (ii.) gravity has an
effect on the liquid/vapor motion, and (iii.) oscillations stopped when the PHP is in a horizontal
orientation. Moreover, they found a complete stop-over configuration, not previously noted in
multi-turn loops, from which they inferred that more turns in the PHP architecture increases the
number of flow perturbations and is necessary for the pulsating behavior. Experiments by
Khandekar and co-workers (Khandekar et al., 2003a-c) have explored other aspects of PHPs.
They report fill ratios between 25-65% are needed to observe pulsating behavior, and that device
orientation with respect to gravity is important. Their findings also suggest a minimum number
of turns are needed to improve device operation. In Khandekar et al., 2003c, they construct a
qualitative map of flow regions observed with respect to inclination angle and heat load. Ma and
co-workers have also conducted experimental studies of PHPs, especially with respect to the
beneficial use of nanoparticles (Ma et al., 2006a, 2006b) and issues regarding device start-up
(Qu and Ma, 2007). More recently, this group has recorded video images using neutron
radiography of a working PHP (Wilson et al., 2008). Thompson et al. (2011a) report
experimental measurements from a three-dimensional “flat” (i.e. channels formed in a solid
substrate, as opposed to a tubular design) heat pipe with heat fluxes as high as 300 W/cm2. Their
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configuration utilized heating and cooling areas that sum to greater than 80% of the total
planform area, which is impractical as a heat pipe device for long-range cooling applications.
Past modeling efforts are based on the idea of describing PHPs by a train of liquid slugs
separated by vapor bubbles confined in a tube and then constructing control volume conservation
relations for each discrete phase (Shafii et al., 2001; Zuo et al.,2001; Zhang and Faghri, 2002;
Zhang et al., 2002; Zhang and Faghri, 2003, Yuan et al., 2010). These models attempt to
describe a variety of physical configurations and phenomena, including evaporation and heat
conduction in the liquid slugs. Shaffii et al. considered both closed looped and open loop PHPs,
and their model can accommodate many vapor bubbles and liquid slugs, although they show a
majority of results for three bubbles. Typical of these mathematical models, they produce
periodic variations in temperature and pressure from which one can calculate both angular
frequencies of pulsation and the total heat transferred from evaporator to condenser; reported
thermal efficiencies are less than those demonstrated by either Zuo et al. (2001) or Wilson et al.
(2008). Zhang and Faghri (2002) describe a similar model, though they assume the vapor phase
is saturated at all times, whereas Shaffii et al. construct a mass transfer model driven by the
difference between the bubble and local wall temperatures. Nikolayev (2011) recently extended
like models by proposing an evaporation rate based on an interfacial heat balance; a similar idea
is applied in this work and described in Section 2.3. Nikolayev’s model displays intermittent
behavior as is seen in experimental visualizations, an improvement to the Zhang models which
demonstrate strictly periodic behavior. Most modeling studies conclude that a majority of energy
transferred by a PHP is by sensible heat, with latent heat effects providing the motive force for
motion, but not responsible for much of the net heat transfer.
Although the models proposed to date include some relevant mechanisms for describing PHP
operation, they also neglect a few. Most models are one-dimensional and comprised of coupled
sub-models to represent bubbles and liquid slugs. In addition, they ignore heat transfer with the
confining materials, be it tubing or solid substrate. None of the cited models consider bubble